The Discrete Collision-Induced Breakage Equation with Mass Transfer: Well-Posedness and Stationary Solutions

.The discrete collisional breakage equation, which captures the dynamics of cluster growth when clusters undergo binary collisions with possible matter transfer, is discussed in this article. The existence of global mass-conserving solutions is investigated for the collision kernels \(ai,j=A(iα jβ + iβjα)\), \(i, j ≥ 1\), with \(α ∈ (-∞,1)\), \(β ∈ [α,1]∩ (0,1]\), and \(A> 0\) and for a large class of possibly unbounded daughter distribution functions. All algebraic superlinear moments of these solutions are bounded on time intervals \([T,∞ )\) for any \(T> 0\). The uniqueness issue is further handled under additional restrictions on the initial data. Finally, nontrivial stationary solutions are constructed by a dynamical approach.Keywordscollision-induced fragmentation equationwell-posednessmass-conservationpropagation of momentsstationary solutionsMSC codes34A1234C1137C25